MCQ in Age, Work, Mixture, Digit, Motion Problems Part 1 | Math Board Exam

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Future License Engineers, these aren’t just random exercises—they’re the EXACT type of questions that separate top-scoring examinees from average performers. This Multiple Choice Questions (Part 1) series focuses on Age, Work, Mixture, Digit, and Motion Problems—critical areas where points are won or lost on the Engineering Board Exam.

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MCQ Topic Outline included in Mathematics Board Exam Syllabi

• MCQ in Age Problems MCQ in Work Problems | MCQ in Mixture Problems | MCQ in Digit Problems | MCQ in Age Problems | MCQ in Motion Problems

Start Practice Exam Test Questions Part 1 of the Series

Choose the letter of the best answer in each questions.

Problem 1: ECE Board April 1995

Kayla is 24 years. Kayla is twice as old as Erin when Kayla was as old as Erin is now. How old is Erin now?

A. 16

B. 18

C. 12

D. 15

Problem 2: EE Board April 1997

The sum of Kim’s and Kevin’s ages is 18. In 3 years, Kim will be as twice as old as Kevin. What are their ages now?

A. 4, 14

B. 5, 13

C. 7, 11

D. 6, 12

Problem 3: GE Board February 1994

Robert is 15 years older than his brother Stan. However “y” years ago, Robert was twice as old as Stan. If Stan is now “b” years old and b>y, find the value of (b – y).

A. 15

B. 16

C. 17

D. 18

Problem 4:

John is 3 times as old as Jaime. Three years ago, John was four times as old as Jaime. The sum of their ages is?

A. 20

B. 24

C. 28

D. 36

Problem 5:

A girl, is one-third as old as her brother and 8 years younger than her sister. The sum of their ages is 38 years. How old is the girl?

A. 4

B. 5

C. 6

D. 7

Problem 6:

Maja is now 18 years old and his colleague Angel is 14 years old. How many years ago was Maja twice as old as Angel?

A. 5

B. 7

C. 8

D. 10

Problem 7:

A father tells his son, I was your age now when you were born”. If the father is now 38 years old, how old was his son 2 years ago?

A. 15

B. 17

C. 19

D. 21

Problem 8:

Six years ago, Maya was five times as old Richard. In five years, Maya will be three times as old as Richard. What is the present age of Richard?

A. 17

B. 16

C. 15

D. 14

Problem 9:

At present, the sum of the parents’ ages is twice the sum of the children’s ages. Five years ago, the sum of the parent’s ages was 4 times the sum of the children’s ages. Fifteen years hence, the sum of the parents’ ages will be equal to the sum of the children’s ages. How many children are there?

A. 3

B. 4

C. 5

D. 6

Problem 10:

Tom is now twice as old as Jerry. Four years ago, Tom was three times as old as Jerry then. How old is Tom?

A. 14

B. 16

C. 18

D. 24

Problem 11: ME Board February 1998

A pump can pump out water from a tank in 11 hours. Another pump can pump out water from the same tank in 20 hours. How long will it take both pumps to pump out water in the tank?

A. 7 hours

B. 6 hours

C. 7 1/2 hours

D. 6 1/2 hours

Problem 12: CE Board November 1993

A 400-mm pipe can fill the tank alone in 5 hours and another 600-mm pipe can fill the tank alone in 4 hours. A drain pipe 300-mm can empty the tank in 20 hours. With all the three pipes open, how long will it take to fill the tank?

A. 2.00 hours

B. 2.50 hours

C. 2.25 hours

D. 2.75 hours

Problem 13:

A tank is filled with an intake pipe in 2 hours and empties by an outlet pipe in 4 hours. If both pipes are opened, how long will it take to fill the empty tank?

A. 3 hours

B. 4 hours

C. 5 hours

D. 6 hours

Problem 14:

A tank can be filled in 9 hours by one pipe, 12 hours by a second pipe and can be drained when full by a third pipe in 15 hours. How long will it take to fill an empty tank with all pipes in operation?

A. 7 hours and 12 minutes

B. 7 hours and 32 minutes

C. 7 hours and 42 minutes

D. 7 hours and 50 minutes

Problem 15: ME Board April 1995

If A can do the work in “x” days and B in “y” days, how long will they finish the job working together?

A.

B.

C.

D.

Problem 16: ECE Board November 1995

Pedro can paint a fence 50% faster than Juan and 20% faster than Pilar, and together they can paint a given fence in 4 hours. How long will it take Pedro can paint the same fence if he had to work alone?

A. 6

B. 8

C. 10

D. 12

Problem 17:

Glenn can paint a house in 9 hours while Stewart can paint the same house in 16 hours. They work together for 4 hours. After 4 hours, Stewart left and Glenn finished the job alone. How many more days did it take Glenn to finish the job?

A. 2.75 hours

B. 2.50 hours

C. 2.25 hours

D. 3.00 hours

Problem 18: CE Board November 1993

It takes Butch twice as long as it takes Dan to do a certain piece of work. Working together they can do the work in 6 days. How long would it take Dan to do it alone?

A. 9 days

B. 10 days

C. 11 days

D. 12 days

Problem 19: ME Board April 1995

John and Peter working together can finish painting a house in 6 days. John working alone can finish it in 5 days less than Peter. How long will it take each of them to finish the work alone?

A. 8, 13

B. 10, 15

C. 6, 11

D. 7, 12

Problem 20: EE Board April 1996

Ron and Rej can do a piece of work in 42 days, Rej and Loyd in 31 days and Loyd and Ron in 20 days. In how many days can all of them do the work together?

A. 19

B. 17

C. 21

D. 15

Problem 21:

It takes Jannah twice as long as Cathy to do a certain piece of work. Working together, they can finish the work in 6 hours. How long would it take Cathy to do it alone?

A. 9 hours

B. 18 hours

C. 12 hours

D. 14 hours

Problem 22: ECE Board April 1999

Vryan, Mike, and Kim can mow the lawn in 4, 6, and 7 hours respectively. What fraction of the yard can they mow in 1 hour if they work together?

A. 47/84

B. 45/84

C. 84/47

D. 39/60

Problem 23:

A farmer can plow the field in 8 days. After working for 3 days, his son joins him and together they plow the field in 3 more days. How many days will it require for the son to plow the field alone?

A. 10

B. 11

C. 12

D. 13

Problem 24: ECE Board November 1991

Crew No. 1 can finish installation of an antenna tower in 200 man-hour while Crew No. 2 can finish the same job in 300 man-hour. How long will it take both crews to finish the same job, working together?

A. 100 man-hour

B. 120 man-hour

C. 140 man-hour

D. 160 man-hour

Problem 25: ME Board October 1991

On one job, two power shovels excavate 20,000 cubic meters of earth, the larger shovel working 40 hours and the smaller for 35 hours. On another job, they removed 40,000 cubic meters with the larger shovel working 70 hours and the smaller working 90 hours. How much earth can each remove in 1 hour working alone?

A. 169.2, 287.3

B. 178.3, 294.1

C. 173.9, 347.8

D. 200.1, 312.4

Problem 26: EE Board October 1997

Ten liters of 25% salt solution and 15 liters of 35% salt solution are poured into a drum originally containing 30 liters of 10% solution. What is the percent concentration of salt in the mixture?

A. 19.55%

B. 22.15%

C. 27.05%

D. 25.72%

Problem 27: ME Board October 1992

A Chemist of a distillery experimented on two alcohol solutions of different strength, 35% alcohol and 50% alcohol, respectively. How many cubic meters of each strength must he use to produce mixture of 60 cubic meters that contain 40% alcohol?

A. 20 m³ of solution with 35% alcohol, 40 m³ of solution with 50% alcohol

B. 50 m³ of solution with 35% alcohol, 20 m³ of solution with 50% alcohol

C. 20 m³ of solution with 35% alcohol, 50 m³ of solution with 50% alcohol

D. 40 m³ of solution with 35% alcohol, 20 m³ of solution with 50% alcohol

Problem 28:

A goldsmith has two alloys of gold, the first being 70% pure and the second being 60% pure. How many ounces of the 60% pure gold must be used to make 100 ounces of an alloy which will be 66% gold?

A. 40

B. 35

C. 45

D. 38

Problem 29: ME Board October 1994

Two thousand (2000) kg of steel containing 8% nickel is to be made by mixing a steel containing 14% nickel with another containing 6% nickel. How much of each is needed?

A. 1500 kg of steel with 14% nickel, 500 kg of steel with 6% nickel

B. 750 kg of steel with 14% nickel, 1250 kg of steel with 6% nickel

C. 500 kg of steel with 14% nickel, 1500 kg of steel with 6% nickel

D. 1250 kg of steel with 14% nickel, 750 kg of steel with 6% nickel

Problem 30:

How much water must be evaporated from 10 kg solution which has 4% salt to make a solution of 10% salt?

A. 4 kg

B. 5 kg

C. 6 kg

D. 7 kg

Problem 31: EE Board October 1994

If a two digit number has x for its unit’s digit and y for its ten’s digit, represent the number.

A. 10x + y

B. 10y + x

C. yx

D. xy

Problem 32: EE Board October 1994

One number is 5 less that the other. If their sum is 135, what are the numbers?

A. 85, 50

B. 80, 55

C. 70, 65

D. 75, 60

Problem 33: ECE Board March 1996

Ten less than four times a certain number is 14. Determine the number.

A. 6

B. 7

C. 8

D. 9

Problem 34: ECE Board March 1996

The sum of the two numbers is 21 and one number is twice the other. Find the numbers.

A. 6, 15

B. 7, 14

C. 8, 13

D. 9, 12

Problem 35: EE Board April 1993

If eight is added to the product of nine and the numerical number, the sum is seventy-one. Find the unknown number.

A. 5

B. 6

C. 7

D. 8

Problem 36:

Find the fraction such that if 2 is subtracted from its term becomes ¼, but if 4 is added to its terms it becomes ½.

A. 3/5

B. 5/12

C. 5/14

D. 6/13

Problem 37: GE Board February 1992

The product of 1/4 and 1/5 of a number is 500. What is the number?

A. 50

B. 75

C. 100

D. 125

Problem 38:

If 3 is subtracted from the numerator of a certain fraction, the value of the fraction becomes 3/5. If 1 is subtracted from the denominator of the same fraction, it becomes 2/3. Find the original fraction.

A. 35/55

B. 36/55

C. 3/7

D. 32/41

Problem 39: ECE Board November 1997

The denominator of a certain fraction is three more than twice the numerator. If 7 is added to both terms of the fraction, the resulting fraction is 3/5. Find the original fraction.

A. 8/5

B. 13/5

C. 5/13

D. 3/5

Problem 40:

Find the product of two numbers such that twice the first added to the second equals 19 and three times the first is 21 more than the second.

A. 24

B. 32

C. 18

D. 20

Problem 41:

The ten’s digit of a number is 3 less than the unit’s digit. If the number is divided by the sum of the digits, the quotient is 4 and the remainder is 3. What is the original number?

A. 36

B. 47

C. 58

D. 69

Problem 42:

The second of the four numbers is three less than the first the third is four more than the first and the fourth is two more than the third. Find the fourth number if their sum is 35.

A. 10

B. 11

C. 12

D. 13

Problem 43: EE Board April 1997

A jogger starts a course at a steady rate of 8 kph. Five minutes later, a second jogger starts the same course at 10 kph. How long will it take the second jogger to catch the first?

A. 20 min

B. 21 min

C. 22 min

D. 18 min

Problem 44: EE Board April 1997

A boat man rows to a place 4.8 miles with the stream and back in 14 hours, but finds that he can row 14 miles with the stream in the same time as 3 miles against the stream. Find the rate of the stream.

A. 1.5 miles per hour

B. 1 mile per hour

C. 0.8 mile per hour

D. 0.6 mile per hour

Problem 45: ECE Board November 1998

A man rows downstream at the rate of 5 mph and upstream at the rate of 2 mph. How far is downstream should he go if he is to return in 7/4 hours after leaving?

A. 2.5 miles

B. 3.3 miles

C. 3.1 miles

D. 2.7 miles

Problem 46: CE Board November 1994

An airplane flying with the wind, took 2 hours to travel 1000 km and 2.5 hours in flying back. What was the wind velocity in kph?

A. 50

B. 60

C. 70

D. 40

Problem 47: CE Board May 1998

A boat travels downstream in 2/3 of the time as it goes going upstream. If the velocity of the river’s current is 8 kph, determine the velocity of the boat in still water.

A. 40 kph

B. 50 kph

C. 30 kph

D. 60 kph

Problem 48:

Two planes leave Manila for a southern city, a distance of 900 km. Plane A travels at a ground speed of 90 kph faster than the plane B. Plane A arrives in their destination 2 hours and 15 minutes ahead of Plane B. What is the ground speed of Plane A.

A. 205 kph

B. 315 kph

C. 240 kph

D. 287 kph

Problem 49: EE Board April 1997

A train, an hour after starting, meets with an accident which detains it an hour, after which it proceeds at 3/5 of its former rate and arrives three hour after time; but had the accident happened 50 miles farther on the line, it would have arrived one and one-half hour sooner. Find the length of the journey.

A. 910/9 miles

B. 800/9 miles

C. 920/9 miles

D. 850/9 miles

Problem 50:

On a certain trip, Edgar drives 231 km in exactly the same time as Edwin drive 308 km. If Erwin’s rate exceeded that of Edgar by 13 kph, determine the rate of Erwin.

A. 39 kph

B. 44 kph

C. 48 kph

D. 52 kph

Online Questions and Answers in Age, Work, Mixture, Digit, Motion Problems

Following is the list of practice exam test questions in this brand new series:

Mathematics Board Examination Mastery | Math Engineering Pre-Board